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On nondistributive Steiner quasigroups

A. Marczak (1997)

Colloquium Mathematicae

A well known result of R. Dedekind states that a lattice is nonmodular if and only if it has a sublattice isomorphic to N 5 . Similarly a lattice is nondistributive if and only if it has a sublattice isomorphic to N 5 or M 3 (see [11]). Recently a few results in this spirit were obtained involving the number of polynomials of an algebra (see e.g. [1], [3], [5], [6]). In this paper we prove that a nondistributive Steiner quasigroup (G,·) has at least 21 essentially ternary polynomials (which improves the...

On permutability in semigroup varieties

Bedřich Pondělíček (1991)

Mathematica Bohemica

The paper contains characterizations of semigroup varieties whose semigroups with one generator (two generators) are permutable. Here all varieties of regular * -semigroups are described in which each semigroup with two generators is permutable.

On quasivarieties of nilpotent Moufang loops. II

Vasile I. Ursu (2012)

Commentationes Mathematicae Universitatis Carolinae

In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.

On reductive and distributive algebras

Anna B. Romanowska (1999)

Commentationes Mathematicae Universitatis Carolinae

The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left k -step reductive Ω -algebras, and of right n -step reductive Ω -algebras, are independent for any positive integers k and n . This gives a structural description of algebras in the join of...

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